Assessing statistical significance of periodogram peaks

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability.Comment: 7 pages, 6 figures, 1 table; To be published in MNRA

Testing Of Nonstationarities In The Unit Circle,Long Memory Processes And Day Of The Week Effects In Financial Data

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1-Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1-L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and the Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt-5 + εt, implying in both cases that the returns are completely unpredictable. In the case of the Dow Jones index, a model of the form (1-L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behaviour

LASR-Guided Stellar Photometric Variability Subtraction: The Linear Algorithm For Significance Reduction

We develop a technique for removing stellar variability in the light curves of $\delta$-Scuti and similar stars. Our technique, which we name the Linear Algorithm for Significance Reduction (LASR), subtracts oscillations from a time series by minimizing their statistical significance in frequency space. We demonstrate that LASR can subtract variable signals of near-arbitrary complexity and can robustly handle close frequency pairs and overtone frequencies. We demonstrate that our algorithm performs an equivalent fit as prewhitening to the straightforward variable signal of KIC 9700322. We also show that LASR provides a better fit to seismic activity than prewhitening in the case of the complex $\delta$-Scuti KOI-976.Comment: 9 pages, 5 figures, accepted for publication in Astronomy & Astrophysics. Pseudocode and github link to code included in manuscrip

Long Run And Cyclical Dynamics In The Us Stock Market

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases

Testing for periodicities in near-IR light curves of Sgr A

We present the results of near-infrared (2 μm) monitoring of Sgr A*-IR with 1 minute time sampling using laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2006 May and 2007 August. Sgr A*-IR is detected at all times and is continuously variable. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Of particular interest are periods of ~20 min, which corresponds to a quasi-periodic (QPO) signal claimed based upon previous near-infrared observations and interpreted as the orbit of a ’hot spot’ at or near the last stable orbit of a spinning black hole. We investigate these claims by comparing periodograms of the light curves with models for red noise and find no significant deviations that would indicate QPO activity at any time scale probed in the study. We find that the variability of Sgr A* is consistent with a model based on correlated noise with a power spectrum having a frequency dependence of ~ f^(2.5), consistent with that observed in AGNs. Furthermore, the periodograms show power down to the minimum sampling time of 2 min, well below the period of the last stable orbit of a maximally spinning black hole, indicating that the Sgr A*-IR light curves observed in this study is unlikely to be from the Keplerian motion of a single ’hot spot’ of orbiting plasma

A simple test for periodic signals in red noise

We demonstrate a simple method for testing the significance of peaks in the periodogram of red noise data. The procedure was designed to test for spurious periodicities in X-ray light curves of active galaxies, but can be used quite generally to test for periodic components against a background noise spectrum assumed to have a power law shape. The method provides a simple and fast test of the significance of candidate periodic signals in short, well-sampled time series such as those obtained from XMM-Newton observations of Seyfert galaxies, without the need for Monte Carlo simulations. A full account is made of the number of trials and the uncertainties inherent to the model fitting. Ignoring these subtle effects can lead to substantially overestimated significances. These difficulties motivate us to demand high standards of detection (minimum >99.9 per cent confidence) for periodicities in sources that normally show red noise spectra. The method also provides a simple means to estimate the power spectral index, which may be an interesting parameter itself, regardless of the presence/absence of periodicities.Comment: 13 pages. 12 figures. Accepted for publication in A&

A Test for the Difference Parameter of the ARFIMA Model Using the Moving Blocks Bootstrap.

In this paper we construct a test for the difference parameter d in the fractionally integrated autoregressive moving-average (ARFIMA) model. Obtaining estimates by smoothed spectral regression estimation method, we use the moving blocks bootstrap method to construct the test for d. The results of Monte Carlo studies show that this test is generally valid for certain block sizes, and for these block sizes, the test has reasonably good power.Long memory, Periodogram regression, Smoothed periodogram regression, Block size.